Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom.

     

Noise performance of multiplexed fiber-optic sensor systems with optical amplifiers

The signal to noise ratio (SNR) of a multiplexed fiber-optic sensor network can be improved by inserting fiber-optic amplifiers. Several configurations of amplifiers in the sensor network are analyzed. A single fiber-optic amplifier used as a preamplifier is a good solution with high SNR. However, by distributing amplifiers in the network even higher SNR can be obtained, and identical couplers can be used throughout the network.     

Correction to: Fast data-driven model reduction for nonlinear dynamical systems

Nonlinear Dynamics -